Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative
- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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$\frac{d}{dx}\left(\frac{\left(x-1\right)\left(2x-2\right)-2x^2+4x+6}{\left(x-1\right)^{3}}\right)$
Learn how to solve problems step by step online. Find the derivative of d/dx(((x-1)^2(2x-2)-2(x^2-2x+-3)(x-1))/((x-1)^4)). Simplifying. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify \left(\left(x-1\right)^{3}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 2. Simplify the product -(\left(x-1\right)\left(2x-2\right)-2x^2+4x+6).